Stephane Charpinet

The quest for the origin of linear combination frequencies in pulsating stars is critical for mode identification and subsequent seismic modeling. Hybrid γ Doradus (Dor) stars provide a crucial test bed for such investigations due to their rich frequency content in both gravity ( g ) and pressure ( p ) modes. Here, we perform a comprehensive survey of 608 Kepler γ Dor stars, detecting 81 265 frequencies, and identifying 1895 harmonics and 45 968 combinations involving two parent frequencies. Our results suggest that the proportion of linear combinations increases with the frequency number in each γ Dor star, leveling off at approximately 75%. The majority of the parent-to-child amplitude ratios are distributed between 100 and 10 000, peaking between 2000 and 4000. Moreover, the amplitude ratios, involving two g -mode parents, are found to escalate with increasing combination frequency. These values are at least an order of magnitude higher than those predicted by nonlinearity distortion of the light curve, whereas they align well with those of nonlinear resonant coupling. Our findings suggest that a significant portion of combination frequencies are likely intrinsic modes under resonant conditions rather than products of surface geometric distortions, offering new insights that warrant systematic investigations across other types of pulsating star.

The frequency of the pressure (p) mode in δ Scuti stars can exceed the Nyquist limit of Kepler long-cadence photometry. These “superNyquist frequencies” (SNFs) are observed as “reflected” peaks at lower frequencies, i.e., they are Nyquist aliases that pose a threat to asteroseismic diagnostics. Their impact on δ Scuti p modes has yet to be comprehensively explored. We performed a systematic survey to search for SNFs in 1838 Kepler δ Scuti stars through a novel technique based on a sliding Lomb-Scargle periodogram, identifying 15 265 confirmed SNFs in 1309 stars, from a total of 259 883 frequencies. We observe that the total number of detected frequencies per star remains featureless across the δ Scuti instability strip; however, young stars pulsate in higher frequencies and so have significantly more SNFs on average. Both the number and the rate of SNFs diminish accordingly as δ Scuti stars become more evolved, which is consistent with both observation and stellar models. Furthermore, our method detects a greater fraction of modes as SNFs at higher frequencies, rising from approximately 1% at 20 μHz to 23% at the Nyquist limit. The rate of underdetection is highest amongst low-amplitude modes. The SNF modulation patterns can be well distinguished from phase modulations induced by binarity or nonlinear mode interactions. We provide a frequency catalog for future asteroseismic studies of δ Scuti stars, wherein we identify each peak as being real or an alias, enabling further investigations into regular patterns of pulsation modes, linear combination frequencies, and theoretical modeling.

Context. Internal magnetic fields have recently been detected and measured in the radiative core of red giant stars using asteroseismology. As they are one of the progenitors of red giant stars and exhibit high radial order gravity modes, γ Doradus stars may also hold detectable magnetic fields in their radiative envelope. Aims. We aim to detect, for the first time, an internal magnetic field in a rapidly rotating γ Doradus star through its influence on the propagation of Kelvin gravito-inertial modes. Methods. We used the seismic variable δK _a , defined as a combination of Kelvin modes frequencies, which is sensitive to the presence of a magnetic field. Following the detection, we modeled the star oscillation spectrum while considering a magnetic component following a Bayesian approach. Results. We found a magnetic signature in the radiative envelope of KIC 2309579. If located just above the core, in the layers that were previously convective, the magnetic field would reach ∼4 kG.

Context. A large proportion of observed white dwarfs show evidence of debris disks, remnants of the former planetary systems, and/or signatures of heavy elements in their atmospheres, induced by the accretion of planetary matter onto their surfaces. The observed abundances are the result of the balance between the accretion flux and the dilution of this planetary material by internal transport processes. A recent study showed that more massive DA white dwarfs are less polluted than smaller mass ones. It was suggested that the reason could be related to the formation of planetary systems when these stars were on the main sequence. Aims. The aim of this work is to test how internal dilution processes, including thermohaline convection, change with white dwarf masses, and whether such an effect could account for variations in the observed pollution. Methods. We computed the efficiency of atomic diffusion and thermohaline convection after the accretion of heavy elements onto white dwarfs using static DA models with various masses, effective temperatures, and hydrogen contents. Results. We confirm that thermohaline convection is always more efficient in diluting accreted elements than atomic diffusion, as previously shown in the literature. However, we find that element dilution by thermohaline convection is less efficient in massive white dwarfs than in smaller mass ones, due to their larger internal density. Conclusions. We showed that the differences in observed heavy element pollution in white dwarfs according to their masses cannot be explained by the dilution induced by atomic diffusion and thermohaline mixing alone. Indeed, the pollution by planetary system accretion should be more easily detectable in massive white dwarfs than in low-mass ones. We discuss other processes that should be taken into account before drawing any conclusion about the occurrences of planetary systems according to the mass of the star on the main sequence.

Context . Hot subdwarf B (sdB) and O (sdO) type stars are evolved helium-burning objects that lost their hydrogen envelope before the helium flash when their progenitors were close to the tip of the red giant branch (RGB). They populate the extreme horizontal branch (EHB) in the Hertzsprung-Russell diagram (HRD). The mass distribution of canonical hot subdwarfs is expected to peak at the core mass required for helium ignition under degenerate conditions in the 0.45-0.5 M _⊙ range. However, non-degenerate helium ignition from intermediate-mass progenitors and non-canonical pathways, such as the merger of helium white dwarfs and delayed helium flashes, are also expected to contribute to the hot subdwarf population. Aims . Using high-quality, homogeneous spectra of 335 hot subluminous star candidates from the Arizona-Montréal Spectroscopic Survey, we aim to improve our understanding of the atmospheric and stellar properties of hot subdwarf stars. Our focus is on the mass distribution of the different types of hot subdwarfs and their connections to the various formation scenarios. Methods . We used large grids of model atmospheres to fit the observed spectra and derived their atmospheric parameters: effective temperature ( T _eff ), surface gravity, and helium abundance. The model grids were further utilized to fit the spectral energy distribution of each star and the Gaia parallax was used to compute the stellar parameters radius, luminosity, and mass. Results . Our spectroscopic sample mostly consists of H-rich sdBs and sdOs, but also contains 41 He-rich sdOs. Additionally, the sample includes 11 intermediate-helium stars and 19 horizontal branch objects with T _eff > 14 kK. We detected the presence of helium stratification in six sdB stars with T _eff around 30 kK, making them good candidates for also showing ³ He enrichment in their atmospheres. Our sdB distribution along the EHB shows a gap near 33 kK, visible in both the Kiel (log g-T _eff ) diagram and HRD, corroborating previous observations and predictions. The mass distributions of H-rich sdBs and sdOs are similar and centered around 0.47 M _⊙ , consistent with the canonical formation scenario of helium ignition under degenerate conditions. Among the H-rich hot subdwarfs, we found no difference between the mass distributions of close binaries and apparently single stars. The He-sdOs have a significantly wider mass distribution than their H-rich counterparts, with an average mass of about 0.78 M _⊙ . In the HRD, the He-sdOs lie on the theoretical helium main sequence for masses between 0.6 and 1 M _⊙ . This strongly favors a merger origin for these He-rich objects. We identified a small number of candidate low-mass (⊙ ) sdBs located below the EHB that might have originated from more massive progenitors. These low-mass sdBs preferentially show low helium abundances. Finally, we identified more than 80 pulsating stars in our sample and found that they fall into well-defined p - and g -mode instability regions.

Context. The Kepler and TESS space missions have revealed the rich gravity (g-)mode pulsation spectra of many hot subdwarf B (sdB) stars in detail. These spectra exhibit complex behaviors, with some stars exhibiting trapped modes interposing in the asymptotic period sequences of regular period spacing, while others do not. Aims. We aim to thoroughly compute theoretical g-mode pulsation spectra, using our current sdB models, useful for future reference when comparing to observations. This also enables us to explore relationships with features of the internal structure of these stars. Such studies provide guidance in conducting future asteroseismic analyses of these pulsators and insights on how to interpret their outcomes. Methods. We used our STELlar modeling from the Université de Montréal (STELUM) code to compute static (parametric) and evolutionary models of sdB stars, with different prescriptions for their chemical and thermal structures. We used our adiabatic PULSE code to compute the theoretical spectra of g-mode pulsations for degrees of ℓ = 1 to 4 and for periods between 1000 s and 15 000 s, amply covering the range of observed g-modes in these stars. Results. We show that g-mode pulsation spectra and, in particular, the appearance of trapped modes are highly dependent on the chemical and thermal structures in the models as the star evolves, particularly in the region just above the He-burning core. Depending on the prescriptions and specific evolutionary stage, we observe mainly three types of spectra for mid to high radial-order g-modes (the ones observed in sdB stars): “flat” spectra of nearly constant period spacing; spectra with deep minima of the period spacing interposing between modes with more regular spacing (which correspond to trapped modes); and spectra showing a “wavy” pattern in period spacing. For the two latter cases, we have identified the region where the modes are trapped in the star. Conclusions. Detailed comparisons with observed g-mode spectra ought to be carried out next to progress on this issue and constrain the internal structure of core-He burning stars via asteroseismology, in particular, for the region above the He-burning core.

Given their tendency to mix in with real pulsations, the reflection of super-Nyquist frequencies (SNFs) pose a threat to asteroseismic properties. Although SNFs have been studied in several pulsating stars, a systematic survey remains to be explored. Here, we propose a method for identifying SNFs from Kepler and TESS photometry by characterizing their periodic frequency modulations using a sliding Fourier transform. After analyzing long-cadence photometry in the Kepler legacy, we identified 304 SNFs in 56 stars from 45 607 frequencies in ∼600 γ Doradus stars, corresponding to a fraction of approximately 0.67% and 9.2%, respectively. Most SNFs were detected in the frequency range of pressure mode over 120 μHz and the fraction of SNF detection increases as frequency up to ∼7%. We found only two potential SNFs mixed with gravity modes in two γ Doradus stars. These findings indicate that SNFs have a negligible impact on global seismic properties, such as those derived from period spacing in γ Doradus stars. However, we stress that SNFs must be carefully and systematically examined by this method in other pulsating stars, particularly δ Scuti and hot B subdwarf stars, to establish a solid foundation for the precise asteroseismolgy of various types of pulsators.

Context. The Transiting Exoplanet Survey Satellite (TESS) performs high-precision photometry over almost the whole sky primarily in search of exoplanet transits. It also provides exquisite data to study stellar variability, in particular for pulsating hot B subdwarf (sdB) stars. Aims. We present a detailed analysis of a new hybrid (p- and g-mode) sdB pulsator, TIC 441725813 (TYC 4427-1021-1), discovered and monitored by TESS for 670 days. Methods. The TESS light curves available for this star were analysed using prewhitening techniques to extract mode frequencies accurately. The pulsation spectrum was then interpreted through methods that include asymptotic period spacing relationships and the identification of rotational multiplets. We also exploited a high signal-to-noise ratio (S/N), low-resolution spectrum of TIC 441725813 using grids of non-local thermodynamic equilibrium (NLTE) model atmospheres to derive its atmospheric parameters. Results. The light curve analysis reveals that frequencies are mostly found in the g-mode region, but several p-modes are also detected, indicating that TIC 441725813 is a hybrid sdB pulsator. We identify 25 frequencies that can be associated with ℓ = 1 g-modes, 15 frequencies corresponding to ℓ = 2 g-modes, and six frequencies characteristic of p-modes. Interestingly, several frequency multiplets interpreted as rotational splittings of deep-probing g-modes indicate a slow rotation period of at least 85.3 ± 3.6 day, while splittings of mostly envelope-probing p-modes suggest a significantly shorter rotation period of 17.9 ± 0.7 day, which implies the core (mainly the helium mantle with possibly the deeper partially mixed helium-burning core that it surrounds) rotates at least 4.7 times slower than the envelope. The radial velocity curves indicate that TIC 441725813 is in a close binary system with a low-luminosity companion, possibly a white dwarf. While elusive in the available TESS photometry, a low-frequency signal that would correspond to a period of ∼6.7 h is found, albeit at a low S/N. Furthermore, we estimate the inclination angle to be ∼60° by two independent means. Conclusions. TIC 441725813 is a particularly interesting sdB star whose envelope rotates faster than the core. We hypothesise that this might be caused by the effects of a tidal interaction with a companion, although in the present case, the presence of such a companion will have to be further investigated. This analysis paves the way towards a more detailed seismic probing of TIC 441725813 using optimisation techniques, which will be presented in a second paper.

Stellar flares are critical phenomena on stellar surfaces, which are closely tied to stellar magnetism. While extensively studied in main-sequence (MS) stars, their occurrence in evolved compact stars, specifically hot subdwarfs and white dwarfs (WDs), remains scarcely explored. Based on Cycles 1–5 of TESS photometry, we conducted a pioneering survey of flare events in ∼12,000 compact stars, corresponding to ∼38,000 light curves with a 2 minute cadence. Through dedicated techniques for detrending light curves, identifying preliminary flare candidates, and validating them via machine learning, we established a catalog of 1016 flares from 193 compact stars, including 182 from 58 sdB/sdO stars and 834 from 135 WDs, respectively. However, all flaring compact stars showed signs of contamination from nearby objects or companion stars, preventing sole attribution of the detected flares. For WDs, it is highly probable that the flares originated from their cool MS companions. In contrast, the higher luminosities of sdB/sdO stars diminish companion contributions, suggesting that detected flares originated from sdB/sdO stars themselves or through close magnetic interactions with companions. Focusing on a refined sample of 23 flares from 13 sdB/sdO stars, we found their flare frequency distributions were slightly divergent from those of cool MS stars; instead, they resemble those of hot B/A-type MS stars having radiative envelopes. This similarity implies that the flares on sdB/sdO stars, if these flares did originate from them, may share underlying mechanisms with hot MS stars, which warrants further investigation.

We briefly review progress in developing a pathway to nonlinear astereoseismology, both from theoretical and observational aspects. As predicted by the theory of weak nonlinear interactions between resonant modes, their amplitude and frequency can be modulated according to various kinds of patterns. However, those subtle modulations could hardly be well characterized from ground-based photometric monitoring. The {\sl Kepler} spacecraft offered a new window to find clear-cut evidence of well-determined amplitude and frequency modulations, leading to the first discoveries of such variations in pulsating white dwarf and hot B subdwarf stars. Following that direction, a systematic survey of oscillation mode properties in compact pulsators monitored by {\sl Kepler} suggests that mode variability is likely a common phenomenon, which remain unaccounted for by standard linear non-radial pulsation theory. To reach this conclusion firmly, the survey has now been extended to a larger context including compact stars observed by K2 and TESS. We expect that this extended survey will help to constrain key parameters governing weak nonlinear effects in stellar oscillations.